If the property is inside the scheme area and rented out under most types of tenancy, the landlord usually needs a licence. That includes a couple renting a flat, a single tenant renting a whole house, and a family renting a terrace.
A selective licence does not normally apply to social housing, holiday lets, properties under the Housing Act 1985 Part 7, or homes already licensed as HMOs. The council's notice of designation lists the exact exemptions, and they vary scheme to scheme.
Whoever is in control of the property is responsible for the licence. That is normally the freeholder for a house, or the leaseholder for a flat. A managing agent can hold the licence with the landlord's written agreement.